A\mathscr{A}-Schemes and Zariski-Riemann Spaces

  • Satoshi Takagi

    Osaka City University, Japan


In this paper, we will investigate further properties of A\mathscr{A}-schemes introduced in [Tak]. The category of A\mathscr{A}-schemes possesses many properties of the category of coherent schemes, and in addition, it is co-complete and complete. There is the universal compactification, namely, the Zariski-Riemann space in the category of A\mathscr{A}-schemes. We compare it with the classical Zariski-Riemann space, and characterize the latter by a left adjoint.

Cite this article

Satoshi Takagi, A\mathscr{A}-Schemes and Zariski-Riemann Spaces. Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 121–177

DOI 10.4171/RSMUP/127-8